$\begingroup$This question is missing a lot of context/is ill-specified. Brownian motion (a.k.a. Wiener process) has variance $\operatorname{Var}(W_t) = t$, which is nonzero for any $t > 0$. Are you asking if it's possible to make an Ito process with variance zero? In this case, the answer is yes: $dX_t = \mu dt + 0 dW_t$.$\endgroup$
– parsiadApr 18 at 1:09

$\begingroup$Thanks for the reply. Will improve that. So, we are left with dXt = mdt. Let's have m = 0.03. In this case, does its value same as the future value of a fund, for instance, St+1 = St(1.03)?$\endgroup$
– Raihana NasirApr 18 at 1:14